When I paired my cat with a friend's, they got along so well that as long as they were fed, they didn't give a fuck if people were around at all.
Alone, that cat would have missed attention, but done okay.

I think your cats would probably get over it if they had to spend a week in a cat hotel or maybe they wouldn't. I for one would be nervous about leaving them on their own for a week with no one checking on them. If You did that then you'd probably worry and think about them to much when your on playa. If you leave them to fend for themselves and godforbid something happened you'd probably feel really bad forever. Or they might just throw a huge party and trash your place...and that would suck too.

We have 3 dogs, 3 cats, 2 parrots, 4 turtles and an iguana. The mastiff/shepherd mix we have had since he was 6 weeks old now tries to rip the throat out of the long haired German shepherd we rescued 4 years ago so they cannot be in the same room or even see each other through the windows or chaos ensues and we have to rotate them daily to my daughters house 1/2 miles away. Have been trying serious training and following the recommendations of the dog whisperer and still no luck. Each dog is absolutely amazing on their own but together.....impossible. Which ever one is here sleeps on our bed with the miniature toy poodle.Then we have a neutered female kitty that we have had since she was 6 weeks old but the house we live in came with 2 cats, one of which is still alive, probably at least 10 years old, and we now got him to come in but our female does not like it one bit and is always hissing and growling and that is not exactly soothing. Our neighbors cat has decided she likes us more than them and now stays in our house over night so our cat sleeps in our room while the other 2 sleep in the living room but god forbid if my husband lets our cat out before putting the others out because fur will fly. And if that weren't enough we have the 2 seriously crazy parrots, a 20 year old blue and gold macaw and an 18 year old Goffins cockatoo. Taz the macaw loves people with blond hair but not people with dark hair and screams like a maniac if anyone goes behind our house by the river, especially tractors, which happens quite frequently since we live in a peach orchard. If she loves you she will scream all the time to get your attention and if she does not like you she will try to bite you any time you get close enough! Chichi the cockatoo scolds you like a tyrant if you wake her up by making ANY noise in the house past 9:00 PM which in an active household is pretty much impossible but on the other hand she dances like a fiend if she likes the music you are listening to. Try finding someone to manage all of them at once:-((

Yes, I know I must be a glutton for punishment but they do all bring us more joy than grief so it is worth it for us. I actually remodeled my house so I could have more to offer someone that we could get for pet sitting, no joke! We have a hot tub and live right on the Columbia River in the gorge in an area that windsurfers call "the wall" with the only private beach around so usually we get board heads that are happy to deal with the critter drama for the opportunity to spend a good week on the river especially Labor Day or Memorial day when we go to Sasquatch. I advertise for pet lovers who windsurf or sail. April dates for Coachella are more difficult and we appeal to people who fish to watch our animals for that week. Then I don't have to pay someone a million dollars to watch all these beasts:-) So far it has worked out pretty good and we take the dogs and birds with us when we can although we sort of look like a traveling cirucus!

I'm sure it's been suggested, but i'll chime in anyway. I have 2 big dogs, and they are my kids. Leaving them for a week is really rough. Since they have never spent a night alone, I got on care.com to find an overnight dogsitter. It's the best money I spend on Burning Man (beyond my ticket.) She has become a friend of mine, and since I'm traveling more aside from BM, she makes herself available when I give her travel dates.

For people with cats, you could just do a daily check-in, and probably get away with $10/day. For my overnight dog sitter, I pay her $30/day and I leave her $100 for food so she can have what she wants while I'm gone. It costs me $400 for the Burn, but I don't have one moment of worry about my girls. My dog sitter may be extraordinary, she doesn't have another job and essentially moves into my house while I'm gone. When she pulls up the dogs go nuts with excitement. She's worth every last penny.